Olaf is standing on a sheet of ice that covers the football stadium parking lot in Buffalo, New York; there is negligible friction between his feet and the ice. A friend throws Olaf a ball of mass 0.400 kg that is traveling horizontally at 10.4 m/s. Olaf's mass is 67.8 kg.

If Olaf catches the ball, with what speed do Olaf and the ball move afterward?

momentum is conserved.

momentumball= momentumballandOlaf
mb*vb=(mb+mo)V
solve for V

If the ball hits Olaf and bounces off his chest horizontally at 8.10m/s in the opposite direction, what is his speed vf after the collision?

Ans. mball*Vi1+molaf*Vi2=mball*Vf1+molaf*Vf2

Solve for Vf2 ( you have all the other variables given)

Side note: Since Olaf wasn't moving initially, molaf*Vi2 = 0

Well, if there's negligible friction between Olaf's feet and the ice, then there's not much stopping him from becoming the next ice-skating champion! When he catches the ball, according to the laws of physics, the momentum of the system is conserved.

So, let's calculate the initial momentum of the ball:
Momentum_initial = mass_ball x velocity_ball = 0.400 kg x 10.4 m/s

And the initial momentum of Olaf:
Momentum_Olaf_initial = mass_Olaf x velocity_Olaf = 67.8 kg x 0 m/s (since he's initially at rest)

Since momentum is conserved, the total momentum after Olaf catches the ball should be equal to the initial momentum:

Momentum_total_final = Momentum_initial + Momentum_Olaf_initial

Now, Olaf and the ball move together after he catches it, so they will have the same final velocity, which we can call V_final.

Momentum_total_final = (mass_ball + mass_Olaf) x V_final

Solving for V_final:

V_final = Momentum_total_final / (mass_ball + mass_Olaf)

Plug in the values and calculate, and you'll find the speed at which Olaf and the ball move together afterward!

But hey, if you ask me, Olaf might have a faster career in figure skating than football catching!

To determine the speed at which Olaf and the ball move afterward, we can use the principle of conservation of momentum. According to this principle, the total momentum before the catch should be equal to the total momentum after the catch.

Before the catch, the ball is traveling horizontally at 10.4 m/s. Olaf, on the other hand, is initially at rest. Thus, the initial momentum of the ball is given by:

Initial momentum of the ball = mass of the ball × velocity of the ball = 0.400 kg × 10.4 m/s

Since Olaf is initially at rest, his initial momentum is zero:

Initial momentum of Olaf = mass of Olaf × velocity of Olaf = 67.8 kg × 0 m/s

When Olaf catches the ball, both Olaf and the ball move together. Let's call the final velocity of Olaf and the ball as v.

After the catch, the momentum of Olaf and the ball combined is given by:

Final momentum of Olaf and the ball = (mass of Olaf + mass of ball) × final velocity

According to the conservation of momentum principle, the initial momentum is equal to the final momentum:

Initial momentum = Final momentum
0.400 kg × 10.4 m/s + 67.8 kg × 0 m/s = (67.8 kg + 0.400 kg) × v

Now, we can solve the equation to find the final velocity (v).

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